What is the value of (tan(80))/(tan(100)) ?

The value of (tan(80))/(tan(100)) is -1

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(tan(80))/(tan(100))

\frac{tan ( 8 0 ^{\circ} )}{tan ( 10 0 ^{\circ} )}

- 1

Solution steps

\frac{tan ( 8 0 ^{\circ} )}{tan ( 10 0 ^{\circ} )}

Rewrite using trig identities:

tan (8 0^{\circ}) = - tan (10 0^{\circ})

tan (8 0^{\circ})

Use the following identity:

tan (x) = - tan (18 0^{\circ} - x)

tan (x)

Use the following property:

tan (θ) = - tan (- θ)

tan (x) = - tan (- x)

= - tan (- x)

Apply the periodicity of

tan

tan (18 0^{\circ} + θ) = tan (θ)

- tan (- x) = - tan (18 0^{\circ} - x)

= - tan (18 0^{\circ} - x)

= - tan (36 0^{\circ} - 8 0^{\circ})

Simplify

= - tan (28 0^{\circ})

tan (28 0^{\circ}) = tan (10 0^{\circ})

tan (28 0^{\circ})

Rewrite

28 0^{\circ}

18 0^{\circ} + 10 0^{\circ}

= tan (18 0^{\circ} + 10 0^{\circ})

Apply the periodicity of

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 10 0^{\circ}) = tan (10 0^{\circ})

= tan (10 0^{\circ})

= - tan (10 0^{\circ})

= \frac{- tan ( 10 0 ^{\circ} )}{tan ( 10 0 ^{\circ} )}

Simplify

= - 1

\frac{sin ( \frac{35}{25} ) π}{6}

2 cos^{2} (3 7^{\circ}) - 1

- 2 (3.27) - e^{- 0.54} sin (3.27)

sec (3 0^{\circ}) - csc (2 4^{\circ})

12 sin (5 5^{\circ})

What is the value of (tan(80))/(tan(100)) ?
The value of (tan(80))/(tan(100)) is -1